A closer look at some new identities
We obtain infinite products related to the concept of visible from the origin point vectors. Among these is ∏k=3∞(1−Z)φ,(k)/k=11−Zexp(Z32(1−Z)2−12Z−12Z(1−Z)), |Z|<1, in which φ3(k) denotes for fixed k, the number of positive integer solutions of (a,b,k)=1 where a<b<k, assuming (a,b,k) is...
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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171298000805 |
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| _version_ | 1832558570024992768 |
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| author | Geoffrey B. Campbell |
| author_facet | Geoffrey B. Campbell |
| author_sort | Geoffrey B. Campbell |
| collection | DOAJ |
| description | We obtain infinite products related to the concept of visible from the origin point vectors.
Among these is
∏k=3∞(1−Z)φ,(k)/k=11−Zexp(Z32(1−Z)2−12Z−12Z(1−Z)), |Z|<1,
in which φ3(k) denotes for fixed k, the number of positive integer solutions of (a,b,k)=1 where
a<b<k, assuming (a,b,k) is the gcd(a,b,k). |
| format | Article |
| id | doaj-art-186481fe387d4e52be11b66ac505fabb |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-186481fe387d4e52be11b66ac505fabb2025-02-03T01:32:03ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121358158610.1155/S0161171298000805A closer look at some new identitiesGeoffrey B. Campbell0Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, AustraliaWe obtain infinite products related to the concept of visible from the origin point vectors. Among these is ∏k=3∞(1−Z)φ,(k)/k=11−Zexp(Z32(1−Z)2−12Z−12Z(1−Z)), |Z|<1, in which φ3(k) denotes for fixed k, the number of positive integer solutions of (a,b,k)=1 where a<b<k, assuming (a,b,k) is the gcd(a,b,k).http://dx.doi.org/10.1155/S0161171298000805Combinatorial identitiesCombinatorial number theoryLattice points in specified regionsPartitions (elementary number theory). |
| spellingShingle | Geoffrey B. Campbell A closer look at some new identities International Journal of Mathematics and Mathematical Sciences Combinatorial identities Combinatorial number theory Lattice points in specified regions Partitions (elementary number theory). |
| title | A closer look at some new identities |
| title_full | A closer look at some new identities |
| title_fullStr | A closer look at some new identities |
| title_full_unstemmed | A closer look at some new identities |
| title_short | A closer look at some new identities |
| title_sort | closer look at some new identities |
| topic | Combinatorial identities Combinatorial number theory Lattice points in specified regions Partitions (elementary number theory). |
| url | http://dx.doi.org/10.1155/S0161171298000805 |
| work_keys_str_mv | AT geoffreybcampbell acloserlookatsomenewidentities AT geoffreybcampbell closerlookatsomenewidentities |